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5-6 Multiplying Fractions
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
5-6 Multiplying Fractions
Warm Up
1. What is of 12?
2. What is of 100?
3. What is of 120?
4. What is of 100?
5. What is of 480?
6
50
60
12__
12__
12__
14 __
14 __
25
120
5-6 Multiplying Fractions
Problem of the Day
Your favorite uncle left one-fifth of his estate to each of his three children and the rest to his favorite charity. If his estate was worth $105,000, how much was given to charity?$42,000
5-6 Multiplying Fractions
MA.6.A.1.2 Multiply and divide fractions…efficiently.
Also MA.6.A.1.3
Sunshine State Standards
5-6 Multiplying Fractions
On average, people spend of their lives asleep. About
of the time they sleep, they dream. What fraction of
a lifetime does a person typically spend dreaming?
1
3__
1
4__
1
4__ 1
3__
• =1
12__
1
3__1
4__
1
4__ 1
3__
One way to find of is to make a model.
Find of .
Notice that there is 1 section where the shading overlaps, and the product of the numerators is 1. Notice that there are 12 sections in the model, and the product of the denominators is 12. You can use these observations to write a rule for multiplying fractions.
5-6 Multiplying Fractions
1
4__ 1
3__
• 1 • 1
4 • 3 _____
1
12__
=
=
Multiply the numerators.Multiply the denominators.
A person typically spends of his or her lifetime dreaming.
1
12__ The answer is in simplest
form.
Helpful Hint
Notice that when you multiply two proper fractions, the product is less than either factor.
5-6 Multiplying Fractions
Additional Example 1A: Multiplying Fractions
Multiply. Write each answer in simplest form.
1
4__ 2
5__• _____=
=
Multiply numerators. Multiply denominators.
2
20__
1 • 2 4 • 5
1
4__ •
2
5__
The GCF of 2 and 20 is 2.
The answer is in simplest form.=1
10__
5-6 Multiplying Fractions
Additional Example 1B: Multiplying Fractions
Multiply. Write each answer in simplest form.
5
7__ 4
15__•
_____
=
=
Use the GCF to simplify the fractions before multiplying. The greatest common factor of 5 and 15 is 5.
4
21__
1 • 4
7 • 3
5
7__ •
4
15__
Multiply numerators. Multiply denominators.
The answer is in simplest form.
1
7__ •
4
3__
1
3
=
5-6 Multiplying Fractions
Additional Example 1C: Multiplying Fractions
Multiply. Write each answer in simplest form.
4
9__ 6
10__• ______=
=
Multiply numerators. Multiply denominators.
24
90__
4 • 6
9 • 10
4
9__ •
6
10__
The GCF of 24 and 90 is 6.
The answer is in simplest form.=4
15__
5-6 Multiplying Fractions
Check It Out: Example 1A
Multiply. Write each answer in simplest form.
15
63__
____
5
21__
3 • 5
7 • 9
3
7__ 5
9__•
5-6 Multiplying Fractions
Check It Out: Example 1B
Multiply. Write each answer in simplest form.
6
14__
____
3
7__
1 • 6
2 • 7
1
2__ 6
7__•
5-6 Multiplying Fractions
Check It Out: Example 1C
5
8__
_____1 • 14 • 1
1
4
__
1
1
2
5__5
8__
2
5__
•
Multiply. Write each answer in simplest form.
1
4
•
5-6 Multiplying Fractions
Additional Example 2A: Evaluating Fraction Expressions
2
5__
1
3__ b •
2
5__
2
5__1
3__ •
_____1 • 23 • 5
2
15__
Substitute for b.1
3__
Multiply.
The answer is in simplest form.
b =
Evaluate the expression b • for each value of b.
Write each answer in simplest form.
5-6 Multiplying Fractions
You can look for a common factor in a numerator and a denominator to determine whether you can simplify before multiplying.
Helpful Hint
5-6 Multiplying Fractions
Additional Example 2B: Evaluating Fraction Expressions
b = 3
8__
b •2
5
__
2
5
__3
8
__ •
_____3 • 14 • 5
3
20
__
Substitute for b.3
8__
Use the GCF to simplify.
The answer is in simplest form.
1
4
2
5
__3
8
__ •
Multiply.
5-6 Multiplying Fractions
Additional Example 2C: Evaluating Fraction Expressions
b = 5
7__ b •
2
5__
2
5__5
7__ •
_____5 • 27 • 5
10
35__
Substitute for b.5
7__
Multiply.
The GCF of 10 and 35 is 5.
The answer is in simplest form.2
7__
5-6 Multiplying Fractions
Check It Out: Example 2A
Evaluate the expression c • for each value of c.
Write each answer in simplest form.
c =
1
4__
1
7__
1 • 17 • 4
1
28__
_____
5-6 Multiplying Fractions
Check It Out: Example 2B
Evaluate the expression c • for each value of c.
Write each answer in simplest form.
c =
1
4__
4
5__
4
20__
•1
4__4
5
__
1
5__
5-6 Multiplying Fractions
Check It Out: Example 2C
Evaluate the expression c • for each value of c.
Write each answer in simplest form.
c =
1
4__
2
3__
2
12__
•1
4__2
3__
1
6__
5-6 Multiplying Fractions
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
5-6 Multiplying Fractions
Lesson Quiz
Multiply. Write each answer in simplest form.
1. 2.
Evaluate the expression x • for each value of
x. Write the answer in simplest form.
3. x = 4. x =
5. At a particular college of the students take a
math class. Of these students, take basic algebra.
What fraction of all students take basic algebra?
3
5__1
4__ •
5
7__3
10__ •
1
8__
4
5__ 1
8__
2
5__
1
4__
3
20__ 3
14__
1
10__ 1
64__
1
10__
5-6 Multiplying Fractions
1. Multiply and identify the answer in simplest form.
A. C.
B. D.
Lesson Quiz for Student Response Systems
5-6 Multiplying Fractions
2. Multiply and identify the answer in simplest form.
A. C.
B. D.
Lesson Quiz for Student Response Systems
5-6 Multiplying Fractions
3. Evaluate the expression
and identify the answer in simplest form.
A. C.
B. D.
Lesson Quiz for Student Response Systems
5-6 Multiplying Fractions
4. Evaluate the expression
and identify the answer in simplest form.
A. C. 1
B. D. 5
Lesson Quiz for Student Response Systems